TYLERGRAYMARK4350_Exam.1.Part.1_Spring.2021

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MARK4350, Exam I Part 1 [93%], Spring 2021, Wurst Instructions: Please type your name below and your answers in the spaces provided. Save the document with your answers and submit to the eLC Assignment dropbox “Exam 1 Part 1 and Part 2” by 2:00 p.m. Today, Feb. 18 and include your name in the file name. Recall the exam is open notes, open book, open class eLC, and individual work. If needed, you can call me at 770-330-3453. Question points are in []. Name____________Tyler Gray_____________________________________________________-- 1) Briefly explain the difference between ordinal and interval scales of measurement. Suppose a questionnaire includes a question asking a respondent to rank 6 brands of a product in terms of preference. Which scale of measurement would apply to a respondent’s responses to that question? [9] The difference between ordinal and interval scales of measurement is that ordinal variables have responses that have an order that matters, like rating something on a scale of 1 to 5, while interval scales have responses where order matters and there are even intervals/measurable differences between different responses, such as the difference between $5 and $10. In ordinal data, it is not reasonable to estimate the difference between a rating of 1 and a rating of 2 because different people may have different definitions, while the difference between $5 and $10 is measurable and definable. If there was a question like this, asking to rank six different brands, it would be ordinal, because there is no way to capture the difference between brand sentiments in rankings for an individual. 2) A large manufacturer of energy drinks is interested in preferences regarding three different flavor versions for a new product. A study is conducted where three independent samples of sizes 200, 225 and 275 are obtained from the northeast, southeast, and southwest respectively . Respondents who were sampled were asked which of the three flavor versions they preferred (version 1, 2, or 3). It is desired to test whether the preference distributions for the three regions are the same using a Chi Square test. Results (including observed frequencies, denoted f o ) appear below. Expected frequencies, denoted fe , are not shown. X 2 =  (f o – f e ) 2 /f e = 58.776, p-value= .000 df=4 a ) Given the above information, what would you conclude regarding whether or not the preference distributions for the three regions are the same at an alpha level of 0.01? Why (be specific about how you arrived at your conclusion)? [9] Based on the above information, we reject the null hypothesis and have significant evidence that there is at least one regional flavoral difference that is significantly different from expected, because the chi square value has a p-value of 0.000, which is significantly lower than our alpha level 0.01.

b) D etermine the expected cell frequency for flavor version 2 in the southwest region for the table. [5] The expected cell frequency for flavor version 2 in the southwest region is 275 / 3 = 91.667. 2 c ) What do the expected frequencies in the test represent, and how are they used in performing the test? Provide a brief conceptual explanation. [9] The expected cell frequencies in the test represent the expected frequency of each response if all flavors were equally liked in all of the regions. They are used in performing the test to determine if the observed results are significantly different from these in the chi square value, which is a summation of the squared differences in observed and expected frequencies divided by expected frequencies, in order to give us an estimate of the variation from the expected frequencies to help us see whether the results are significantly different from our expectation of all being the same. 3) Management of ABC Movie Theaters, Inc. is interested in analyzing the relationship between weekly revenue and advertising expenditures using television, newspapers, and radio. A sample of 51 was obtained and a regression performed with Revenue (in $000) as the dependent variable and the predictors TV ad expenditure (in $000, variable name TV), newspaper ad expenditure (in $000, variable name NP), and radio ad expenditure (in $000, variable name radio). Output appears below.

3 a) Interpret the estimated coefficient for radio advertising expenditure. [7] The estimated coefficient for radio advertising expenditure of 6.445 estimates that assuming all other variables are held constant, on average for every $1000 increase in radio advertising expenditure, there is an expected increase of $6445 in revenue. 3b) Suppose the analysis was conducted using only newspaper advertising expenditure as a predictor (see output below). Interpret the estimated coefficient for NP, and comment on using this result to provide information about the effect of newspaper advertising expenditure on revenue. [7] This estimate estimates that on average, for every $1000 increase in newspaper advertising expense, there is an expected increase of $11145 in revenue if other variables are not in the model. It is not reasonable to use this model and coefficient for the model, because it seems very likely that this new coefficient is inflated due to the lack of the other variables. There is likely a correlation where companies that advertise more in newspapers also advertise more in other avenues and this model fails to accurately apportion that part of the coefficient to those other avenues of advertisement.

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4) A researcher is interested in the relation of sales (Y, in $0000) to sales person experience in years (X1), and gender (X2), for a particular industry. A regression analysis was conducted and the following output resulted from a sample of 80 sales force members. X2 is a 0,1 indicator variable with male as the reference level. State the overall associated fitted/estimated regression function. In addition, interpret each estimated coefficient in the overall fitted regression function. [11] This model and estimates that on average, male salespeople with zero experience will generate on average an estimated $843,430 of sales , with an expected average increase of $25,190 in sales per additional year of experience, and an expected average higher sales of $126,080 for women. The Constant estimates that a male salesman with zero years of experience would generate an average sales of $843,430. The x1 coefficient estimates that on average for every additional year of experience for a salesperson, they’ll generate an additional $25,190 in revenue. The x2 indicator variable estimates that on average, female saleswomen will generate $126,080 more in sales than male salesmen with the same level of experience.

5) The Apex hotel conducted a satisfaction study by having guests fill out a questionnaire that included a question about overall satisfaction measured on a scale from 0=Very Dissatisfied to 100=Very Satisfied. In addition, 4 performance measure questions were included as described below: Q1: My room met my needs (9= completely agree, 1= completely disagree) Q2: The hotel has an efficient layout (9= completely agree, 1= completely disagree) Q3: The hotel staff was friendly (9= completely agree, 1= completely disagree) Q4: The hotel staff was helpful (9= completely agree, 1= completely disagree) A regression analysis was performed using the overall satisfaction measure as the dependent variable and the performance measures as the explanatory variables. Results appear below. The above output shows evidence of an issue in the regression analysis that should be addressed. State the issue, identify evidence indicating presence of the issue, and suggest a remedial measure. [11] There is a very high correlation/collinearity issue between Q3 and Q4. This is an issue because both of these variables are accounting for the same variation so one is unnecessary. The evidence of collinearity is found in the correlation table w the correlation value of 0.973, and the VIF values of higher than 19 for Q3 and Q4. The remedy for this issue would be to remove Q4, because out of the two, Q4 has a higher VIF and a higher p-value that is less significant.

6) A self-explicated conjoint analysis (as shown in class) was conducted regarding the purchase of battery powered toothbrushes. The study involved 2 attributes: brand with 3 levels (Oral B, SpinBrush, Colgate), and price with three levels ($8, $10, $12). Some associated preference ratings and chip allocation results (allocation of 100 chips among attributes) for a respondent (respondent 1) are provided below. (Note the preference rating for SpinBrush has not been provided. You should be able to determine that value). Chip Allocatio n 60 Brand Preference Rating (-5 to +5 scale where -5 is low end of preference, and +5 is high end of preference) Oral B -1 SpinBrus h Colgate +5 40 Price $8 +5 $10 0 $12 -5 6a) Determine the part-worths(utils) for all attribute levels for this respondent (respondent 1). [7] Oral B: -0.6 Spinbrush: 0 Colgate: +3 $8: +2 $10: 0 $12: -2 6b) The study also included a second respondent (respondent 2), and the part-worths (utils) for the second respondent were determined to be as follows: Oral B (1.0), SpinBrush (-0.4), Colgate (-1.0), $8 (4.0), $10 (1.6), $12 (-4.0). Suppose a market shelf consisted of only two products: Oral B at $12 , and Colgate at $8. Determine the total utility for each product for both respondents (show all results below), and using the maximum utility method (as shown in class), estimate share using the two respondents. [11] Respondent 1 Oral B $12: -0.6 – 2 = -2.6 Respondent 1 Colgate $8: 3 + 2 = 5 Respondent 2 Oral B: $12: 1-4 = -3 Respondent 2 Colgate $8: -1 +4 = 3 Respondent 1 and Respondent 2 would both choose the $8 Colgate toothbrush because they have higher utilities. 6c) Which attribute is most important to respondent 2? Why? [7] The price is certainly more important to respondent 2. This is because the part-worths for price values were much higher for this respondent, so their allocation for that variable is much more important and high.

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TYLERGRAYMARK4350_Exam.1.Part.1_Spring.2021

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